Qi: The dimensions of a rectangular region are varying with the time (t) according to: L = 2t2 -8 cm/sec and w = 3t + 6 cm/sec Where (L) is the length and (w) is the width. Find the value of (t) at which the rate of change in area of the rectangle equals 360 cm-/sec

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A: Since you have asked multiple part question, we will solve the first 3 sub part question for you as…

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A: Here are the solutions: We will use L'Hospital rule and differentiate the numerator and denominator…

Q: We have 3 3 27 dx dy = 4 y (x – 1)2 - Select one: True O False

A: Given query is to find statement is true or false.

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A: Solution is given below

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A: To answer the given questions using the given graph.

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Q: 4) The domain of f(x) = 4 cos-(3x- 1) + 5 is 3) If f(x) = 1+ x+x? then f-1(1) = a) 1 d) 2 e) non b)…

A: Since you have posted multiple questions i can do first three questions as per our company…

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Q: B) By using (A), Find lim /-

A: limn→∞1n

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A: I am attaching image so that you understand each and every step.

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A: Let's find.

Q: So  for the last part of the Question is it A. The Root Tests says that the series converges…

A: Apologies for the inconvenience. Here is the complete solution:   Given series is = ∑n=1∞an where…

Q: 7. The function f (x,y,z) = xyz, when subject to the constraint x + 2y + 3z = 72, has one critical…

A: 7. The function f(x, y, z) = xyz, when subject to the constraint x + 2y + 3z = 72, has one critical…

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Q: Evaluate the limit below. 28 – 4x + 7x2 lim -9x² – 4 - 4

A: LetL=limx→∞ 28-4x+7x2-9x2-4Divide N and D by x2L=limx→∞ 28x2-4xx2+7x2x2-9x2x2-4x2L=limx→∞…

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A: To use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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A: We will answer only part c, d and e because you have mentioned to solve only these three.   Complete…

Q: GIVEN : 2x 2х - 2x ) + 6 1 1 f (x) = 1 --x 8 g(x) = 3(x + + 4 h(x) = 6 - || 3 a.lim -4 · f (x) d.lim…

A: For (a),     limx→2-4 f(x)=limx→ 2-41-18xPlug in the value x=2=-41-18· 2=-3

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Q: (5* )csch x²+1 dy if Find dx 1. (a) y = x >0. (ecosh 5x) In Vx +1 )

A: Find your answer below

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Q: Finding Vertical Asymptotes In Exercises 63–68, find any vertical asymptotes of the graph of the…

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Q: '5 If f(x) dx = 8 and f(x) dx = 5.3, find f(x) dx. If f(x) dx = 31 and g(x) dx = 14, find [4f(x) +…

A: 1. ∫17f(x)dx=8 and ∫57f(x)dx=5.32.∫07f(x)dx=31 and ∫07g(x)dx=14

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Q: Part 3. Provide solution in finding the derivatives of the given function 1. y= 4x5-2x + 3x- 10 2. y…

A: Let's find.

Q: 5 dx J 125x2-9 5. 4t.a-2t

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